论文标题
用于重力透镜模拟的球形快速多极法（SFMM）
The spherical Fast Multipole Method (sFMM) for Gravitational Lensing Simulation
论文作者
论文摘要
在本文中，我们提出了一种球形快速多极方法（SFMM），用于射线追踪弯曲天空上的重力镜头（GL）。 SFMM是快速多种方法（FMM）到Sphere $ \ Mathbb s^2 $的非平地扩展，它可以准确地以$ o（n）\ log（n）$的时间复杂性来准确地求解泊松方程，其中$ n $是粒子的数量。发现SFMM的时间复杂性接近$ O（n）$，并且计算精度可以在我们的测试中达到$ 10^{ - 10} $。此外，与快速球形谐波变换（FSHT）相比，SFMM不仅更快，而且更准确，因为它具有保留密度场的高频组件的能力。这些优点使SFMM成为模拟弯曲天空上重力镜头的最佳方法，即即将进行的大区域天空调查，例如Vera Rubin天文台和中国空间站望远镜。
In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and it can accurately solve the Poisson equation with time complexity of $O(N)\log(N)$, where $N$ is the number of particles. It is found that the time complexity of the sFMM is near $O(N)$ and the computational accuracy can reach $10^{-10}$ in our test. In addition, compared with the Fast Spherical Harmonic Transform (FSHT), the sFMM is not only faster but more accurate, as it has the ability to reserve high-frequency components of the density field. These merits make the sFMM an optimum method to simulate the gravitational lensing on a curved sky, which is the case for upcoming large-area sky surveys, such as the Vera Rubin Observatory and the China Space Station Telescope.
